Question: Simplify the following expression: $ x = \dfrac{5}{8} + \dfrac{y + 1}{-3} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3}{-3}$ $ \dfrac{5}{8} \times \dfrac{-3}{-3} = \dfrac{-15}{-24} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{y + 1}{-3} \times \dfrac{8}{8} = \dfrac{8y + 8}{-24} $ Therefore $ x = \dfrac{-15}{-24} + \dfrac{8y + 8}{-24} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-15 + 8y + 8}{-24} $ $x = \dfrac{8y - 7}{-24}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{-8y + 7}{24}$